Magnetization vector inversion method, device and storage medium with amplitude and gradient constraints
By employing magnitude and gradient constraints in magnetization vector inversion and using a three-component model and iterative solution of the objective function, the problem of insufficient edge accuracy in inversion results under Cartesian coordinates was solved, achieving higher accuracy inversion results and evaluation.
Patent Information
- Application Number
- CN202211343505.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-10-31
- Publication Date
- 2025-12-05
- Estimated Expiration
- 2042-10-31
AI Technical Summary
Existing magnetization vector inversion methods in Cartesian coordinates are insufficient in edge accuracy, resulting in low accuracy of inversion results, especially when dealing with the edges of magnetization vector models, which is difficult to meet requirements.
The magnetization vector inversion method with magnitude and gradient constraints is adopted. By acquiring the observation data of the three-component model, the data weighting matrix, sensitivity weighting matrix and sparse Lp constraint matrix of magnitude constraint are calculated to construct the objective function and iteratively solve it until the preset iteration state is reached to generate the inversion result.
It significantly improves the edge accuracy of the inversion model, generates sharp edges, improves the accuracy of the inversion results, and provides a more accurate evaluation by combining RMSE and IOU evaluation factors.
Smart Images
Figure CN115629424B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of data processing technology, and more specifically, to a method, apparatus, and storage medium for magnetization vector inversion with amplitude and gradient constraints. Background Technology
[0002] Magnetic vector inversion (MVI) can be used to obtain the three-dimensional distribution of the shape, location, and magnetization intensity of magnetic targets with remanent magnetism in geophysics, geological and mineral exploration, etc. It has important practical value in spacecraft magnetic distribution research, accurate identification of important military targets, detection of underground ferromagnetic pipelines, detection of unexploded ordnance, and non-destructive testing. In particular, for the identification of dangerous objects such as unexploded ordnance, the high-precision 3D reconstructed shape can assist in accurate identification and reduce the risk of damage.
[0003] In the inversion process, the edge accuracy of the inverted model is crucial for determining the shape of the inverted model. However, the accuracy of 3D MVI in the Cartesian coordinate system is not high enough, especially the processing of model edges, which is far from meeting the requirements. In particular, current methods are powerless to improve the edge accuracy in MVI, resulting in insufficient accuracy of the inversion results. Summary of the Invention
[0004] This application provides a method, apparatus, and storage medium for magnetization vector inversion with amplitude and gradient constraints, aiming to improve the accuracy of the inversion results.
[0005] In a first aspect, embodiments of this application provide a magnetization vector inversion method based on amplitude and gradient constraints, the method comprising:
[0006] Acquire observation data of the three-component model and determine the prediction data of the three-component model, wherein the three-component model is used to describe the magnetization intensity in three Cartesian directions;
[0007] Calculate the data weighting matrix used to describe the data noise level, the sensitivity weighting matrix used to compensate for the attenuation of magnetic data with depth, and the sparse Lp constraint matrix based on the amplitude constraint of the three-component model, respectively.
[0008] Based on the observation data of the three-component model, the data weighting matrix, the sensitivity weighting matrix, and the sparse Lp constraint matrix based on the amplitude constraint of the three-component model, the objective function is determined, wherein the objective function is applied to the gradient solution process of the three-component model;
[0009] The objective function is minimized to obtain the updated three-component model;
[0010] The updated three-component model is iteratively solved until the iterative process reaches a preset iterative state. The trained three-component model is then output, and the inversion result of the observation model is generated using the trained three-component model.
[0011] Optionally, the method further includes:
[0012] Based on the trained three-component model, generate the inversion result;
[0013] The inversion results are evaluated by combining the root mean square error and the cross-union ratio.
[0014] Optionally, the predicted data for the three-component model include:
[0015] Calculate the forward operators in three Cartesian directions;
[0016] The prediction data of the observation model is obtained by multiplying the forward operators of the three Cartesian directions with the three-component model.
[0017] Optionally, calculating the sparse Lp constraint matrix based on the magnitude constraint of the three-component model includes:
[0018] Calculate the amplitude of the three-component model;
[0019] By combining the magnitude of the three-component model with the sparse Lp norm constraint function, a sparse Lp constraint matrix for the magnitude constraint of the three-component model is generated.
[0020] Optionally, the formula for the sparse Lp constraint matrix of the magnitude constraint of the three-component model is:
[0021]
[0022] Where, m amp ε is the amplitude of the three-component model; ε is the second threshold factor; p is the sparsity parameter.
[0023] Optionally, the formula for the sensitivity weighting matrix is:
[0024]
[0025] in,
[0026]
[0027] Among them, J mn Let be the element in the m-th row and n-th column of matrix J; δ is the first threshold factor, which is a relatively small number; F[m] is the forward operator; m is the three-component model; v j Let be the volume of the j-th cube element.
[0028] Optionally, based on the data weighting matrix, the sensitivity weighting matrix, and the sparse Lp constraint matrix based on the amplitude constraint of the three-component model, the objective function is determined as follows:
[0029]
[0030] Where φ refers to the objective function; W d The weighted matrix for the data; W P W is the sensitivity weighting matrix; L_A d is the sparse Lp constraint matrix based on the magnitude constraint of the three-component model; F is the forward operator in three Cartesian directions; m is the three-component model; d obs The observed data for the three-component model; For each regularization term, For the integral volume, For discrete difference operators; m ref This is a reference model.
[0031] Optionally, based on the updated three-component model, iterative solutions are performed until the iterative process reaches a preset iterative state, at which point the trained three-component model is output, including:
[0032] The updated three-component model is iteratively solved until the number of iterations is the maximum number of iterations for the three-component model, at which point the trained three-component model is output.
[0033] Alternatively, iteratively solve the problem based on the updated three-component model until the change in the three-component model is minimized, and then output the trained three-component model.
[0034] Secondly, embodiments of this application provide a magnetization vector inversion device based on amplitude and gradient constraints, the device comprising:
[0035] The acquisition module is used to acquire observation data for the three-component model;
[0036] The prediction data calculation module is used to determine the prediction data of the three-component model, wherein the three-component model is used to describe the magnetization intensity in three Cartesian directions.
[0037] The calculation module is used to calculate the data weighting matrix describing the data noise level, the sensitivity weighting matrix to offset the attenuation of magnetic data with depth, and the sparse Lp constraint matrix based on the amplitude constraint of the three-component model.
[0038] The objective function determination module is used to determine the objective function based on the observation data of the three-component model, the data weighting matrix, the sensitivity weighting matrix, and the sparse Lp constraint matrix based on the magnitude constraint of the three-component model, wherein the objective function is applied to the gradient solution process of the three-component model;
[0039] The update module is used to minimize the objective function to obtain the updated three-component model;
[0040] The iterative solution module is used to perform iterative solution based on the updated three-component model until the iterative process reaches a preset iterative state, output the trained three-component model, and use the trained three-component model to generate the inversion result of the observation model.
[0041] Thirdly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the magnetization vector inversion method based on amplitude and gradient constraints as described in the first aspect of the embodiments.
[0042] Beneficial effects:
[0043] In the magnetization vector inversion process, this method divides the magnetization vector into three directions for simultaneous inversion based on a three-component model. The three-component model is iteratively solved based on an objective function. The objective function includes not only the sensitivity weighting constraint to counteract the attenuation of magnetic data with depth, but also the sparse Lp constraint matrix of the magnitude constraint of the three-component model. By applying this objective function to the gradient of the three-component model, the edge accuracy of the inversion model obtained by the three-component model can be significantly improved, that is, the inversion result can produce sharp edges and the accuracy of the inversion result is higher. Attached Figure Description
[0044] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0045] Figure 1 This is a flowchart of the steps of a magnetization vector inversion method based on amplitude and gradient constraints proposed in an embodiment of this application;
[0046] Figure 2 This is a comparison diagram of the inversion model obtained under different inversion parameters and the real model proposed in an embodiment of this application;
[0047] Figure 3This is a comparison diagram of the inversion model and the real model obtained under different inversion parameters according to an embodiment of this application;
[0048] Figure 4 This is a functional block diagram of a magnetization vector inversion device based on amplitude and gradient constraints proposed in an embodiment of this application. Detailed Implementation
[0049] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0050] Magnetism vector inversion (MVI) has a wide range of applications in geophysics. It can be used in geological and mineral exploration to measure the three-dimensional distribution of the shape, location, and magnetization intensity of magnetic targets with remanence. In addition, it has important practical value in the study of magnetic distribution of spacecraft, accurate identification of important military targets, detection of underground ferromagnetic pipes, detection of unexploded ordnance, and non-destructive testing.
[0051] In the inversion process, the edge accuracy of the inversion model is crucial for determining the shape of the inversion model. However, the traditional magnetization vector inversion method in Cartesian coordinates proposed by scholars Lelievre and Oldenburg may lead to low inversion accuracy due to the non-uniqueness of the solution. Generally, it may converge to an incorrect solution after iterative optimization.
[0052] Therefore, in order to solve the problem that the accuracy of the inversion results generated by the current three-dimensional inversion method in the Cartesian coordinate system is not high enough, especially the edge processing of the obtained inversion model is far from meeting the requirements, this embodiment provides a magnetization vector inversion method based on magnitude and gradient constraints.
[0053] Figure 1 The flowchart illustrates the steps of a magnetization vector inversion method based on amplitude and gradient constraints in an embodiment of this application, as follows: Figure 1 The method may specifically include the following steps:
[0054] S101: Obtain observation data for the three-component model.
[0055] Observational data is data obtained by measuring the underground with instruments. Observational data can be three-dimensional magnetic field data, total magnetic field data, magnetic gradient tensor data, etc.
[0056] The three-component model is used to describe the magnetization in three Cartesian directions. Compared with the magnetic susceptibility inversion method, it has three times more unknown parameters. In practical implementation, the three-component model is first... During initialization, if no prior information is available, the reference model m can be selected based on the prior information. ref Set to zero.
[0057] In practical implementation, the underground area can be divided into discrete 10m×10m×10m cubes, with each cube considered as a unit. Integrating the observation data generated for each unit yields the observation data of the three-component model, denoted as d. obs .
[0058] S102: Determine the prediction data for the three-component model.
[0059] In one feasible implementation, the predicted data of the three-component model can be calculated using a forward modeling method. The calculation process for the predicted data of the three-component model can be as follows:
[0060] First, calculate the forward operators in the three Cartesian directions, i.e., calculate F = [F u ,F v ,F w For example, the forward operator F can be derived from Maxwell's equations. In this embodiment, the calculation method of the forward operator F is not specifically limited.
[0061] Next, based on the product of the forward operators in the three Cartesian directions and the three-component model, the predicted data d of the three-component model is obtained. pre Specifically, it can be expressed as:
[0062]
[0063] S103: Calculate the data weighting matrix used to describe the data noise level, the sensitivity weighting matrix used to offset the attenuation of magnetic data with depth, and the sparse Lp constraint matrix based on the amplitude constraint of the three-component model.
[0064] Wherein, the data weighting matrix W is used to describe the data noise level. d It is generally determined by the reciprocal of the variance σ of the observed data.
[0065] Sensitivity weighting matrix W P Its function is similar to that of a depth-weighted function, used to counteract the attenuation of magnetic data with depth. In one feasible implementation, the formula for calculating the sensitivity weighting matrix can be:
[0066]
[0067] in,
[0068]
[0069] Among them, J mn Let be the element in the m-th row and n-th column of matrix J; δ is the first threshold factor, which is a relatively small number; F[m] is the forward operator; m is the three-component model; v j Let be the volume of the j-th cube element.
[0070] In this embodiment, the sparse Lp constraint matrix W based on the magnitude constraint of the three-component model is determined. L_A Specifically, the method used is: in the sparse Lp norm constraint function W L The model incorporates magnitude constraints for a three-component model and a sparse Lp norm constraint function W. L Approximate to the Lawson norm, it can be expressed as:
[0071]
[0072] In the formula, j refers to the j-th 10m×10m×10m cube unit after partitioning; p is a relatively small number, which is used to prevent the denominator from being 0; P is a parameter that can control the sparsity of the final inversion model. Generally, a larger p value will generate a smooth inversion model, such as p=2; a smaller p value is more likely to obtain a blocky inversion model, such as when the value of p is in the range of [0,1].
[0073] Because without constraints on the three-component model during the inversion process, the non-uniqueness of the inversion solution can easily lead to inconsistencies in the position and shape of the three-component model, resulting in low edge accuracy of the inversion result. Therefore, this embodiment uses a sparse Lp norm constraint function W, which can control the sparsity or sharpness of the model boundary. L When applied to the gradient of a three-component model, it facilitates the generation of sharper edges.
[0074] Furthermore, in this embodiment, to further improve the accuracy of the inversion results, especially to obtain a three-component model that can generate inversion results with higher edge accuracy, the three-component model and its gradient are constrained by a sparse Lp constraint function based on magnitude. That is, the sparse Lp constraint matrix W based on the magnitude constraint of the three-component model is determined. L_A .
[0075] In calculating the sparse Lp constraint matrix W based on the amplitude constraint of the three-component model. L_A First, calculate the amplitude of the three-component model using the following formula:
[0076]
[0077] Then, by combining the magnitude of the three-component model with the sparse Lp norm constraint function, the sparse Lp constraint matrix W of the magnitude constraint of the three-component model is generated. L_A Its formula can be:
[0078]
[0079] Here, ε is the second threshold factor, which is also a relatively small number to prevent the denominator from being 0.
[0080] S104: Determine the objective function based on the observation data of the three-component model, the data weighting matrix, the sensitivity weighting matrix, and the sparse Lp constraint matrix based on the amplitude constraint of the three-component model.
[0081] The objective function in this embodiment is constructed based on the Tikhonov function of the inverse problem, which can be expressed as:
[0082] φ(m)=φ d +βφ m
[0083] subject to φ d <φ d *
[0084] Where, φ d φ represents the data mismatch value. d * φ is the target mismatch value. m It is a regularization term that can integrate prior information; β is a regularization parameter, and β is initially set with an initial value.
[0085] Furthermore, the data mismatch value φ d It is the 2-norm of the observed data and the predicted data calculated by the forward model, which measures the ratio of the observed data to the predicted data in the three-component model. It can be further expressed as:
[0086]
[0087] Where i represents the i-th observation data point.
[0088] Regularization term φ that integrates prior information m This can be further expressed as:
[0089]
[0090] Where, φ s φ x φ y φ z These are the constraint functions of the three-component model and their corresponding gradients in the three Cartesian directions, α.s α x α y α z These are the corresponding coefficients; The integral volume; It is a discrete difference operator; These are the regularization coefficients for each term; It is the sparse Lp constraint matrix W of the sensitivity weighting matrix and the amplitude constraint of the three-component model. L_A The combination of is denoted as:
[0091]
[0092] Therefore, the Tikhonov function φ(m) of the inverse problem can be further expanded to obtain the objective function φ, which can be expressed as:
[0093]
[0094] In this embodiment, the objective function φ includes not only the sensitivity-weighted constraint used to compensate for the depth-dependent attenuation of magnetic data, but also the sparse Lp constraint matrix W for the amplitude constraint of the three-component model. L_A The sparse Lp constraint matrix W based on amplitude constraints L_A Applying this to the gradient of a three-component model can significantly improve the edge accuracy of the final inversion model, resulting in sharper edges and higher accuracy.
[0095] S105: Minimize the objective function to obtain the updated three-component model.
[0096] For example, when actually minimizing the objective function, iterative-reweighed-least-squares (IRLS) and the Gauss-Newton method can be used to calculate the values of the new three-component model and update the initialized three-component model.
[0097] S106: Based on the updated three-component model, perform iterative solution until the iterative process reaches the preset iterative state, output the trained three-component model, and use the trained three-component model to generate the inversion result of the observation model.
[0098] After minimizing the objective function, the updated three-component model is obtained. Then, steps S102-S106 are performed using the updated three-component model to optimize and iterate the three-component model.
[0099] Furthermore, after each minimization of the objective function, in addition to updating the three-component model, it is also necessary to update the regularization parameter β involved in the calculation in the next iteration. Let β be the regularization parameter after each update. * Specifically, first calculate the ratio of the current target mismatch value to the data mismatch value, then multiply the current value of β by this ratio, i.e., β * =βφ d * / φ d .
[0100] In one feasible implementation, during the optimization iteration of the three-component model, when the iteration count reaches the maximum number of iterations for the three-component model, the currently optimized three-component model can be output as the trained three-component model.
[0101] In other implementations, the currently optimized three-component model can be output as the trained three-component model when the change in the three-component model is minimal, or when the change in the three-component model is less than a preset threshold.
[0102] Since the three-component model only describes the magnetization intensity in three Cartesian directions, it is necessary to further obtain an inversion model that includes position, shape, magnetization amplitude and direction based on the three-component model, that is, to obtain the inversion result. The trained three-component model obtained after multiple iterations of optimization can generate inversion results with better accuracy.
[0103] The inversion results are usually evaluated. Currently, the evaluation of inversion results is usually judged by human subjectivity or root mean square error (RMSE). However, human subjectivity has a large error margin, the accuracy of the judgment results is low, and it is easy to make mistakes. RMSE describes the distance between the inverted model and the real model. The smaller the distance, the higher the similarity and the higher the accuracy of the inversion results. However, RMSE cannot evaluate shape similarity well, resulting in insufficient or inaccurate evaluation.
[0104] In one feasible implementation, the magnetization vector inversion method based on amplitude and gradient constraints provided in this embodiment further includes:
[0105] After multiple iterations of optimization, inversion results are generated based on the trained three-component model. Then, the inversion results are evaluated by combining the root mean square error and cross-union ratio, which yields more accurate evaluation results.
[0106] Intersection over Union (IOU) is generally used to evaluate the similarity of two-dimensional or three-dimensional models in computer vision. Usually, the larger the IOU value, the better the similarity in position and shape. The IOU is at its maximum when the inverted model and the real model completely overlap, with a value of 1.
[0107] However, considering that IOU can only evaluate the similarity of shape and position, but not the similarity of magnitude, this embodiment combines RMSE and IOU to evaluate the inversion model and the real model.
[0108] Specifically, the evaluation factor in this embodiment can be expressed as:
[0109]
[0110] In the formula, ε is a very small value, its purpose being to prevent the denominator from being zero. The larger the value of the evaluation factor IRE, the better the accuracy of the inversion results.
[0111] Wherein, IOU can be represented as:
[0112]
[0113] In the formula, I(·) is the indicator function. V is the predicted value of the inversion result. i ε represents the true value of the observation model, and ε is the threshold.
[0114] The formula for calculating RMSE is:
[0115]
[0116] Figure 2 and Figure 3 The diagram shows a comparison between the inversion model obtained under different inversion parameters and the real model provided in this embodiment.
[0117] exist Figure 2 In the diagram, (a), (b), and (c) are slices of the real model in the three Cartesian directions x, y, and z; (d), (e), and (f) are slices of the inverted model 1 in the three Cartesian directions x, y, and z; and (g), (h), and (i) are slices of the inverted model 2 in the three Cartesian directions.
[0118] exist Figure 3 In the diagram, (a), (b), and (c) are slices of the real model in the three Cartesian directions x, y, and z; (d), (e), and (f) are slices of the inverted model 3 in the three Cartesian directions x, y, and z; and (g), (h), and (i) are slices of the inverted model 4 in the three Cartesian directions.
[0119] The evaluation indicators for the four inversion models are shown in Table 1.
[0120] Table 1 Evaluation Indicators of Inversion Results
[0121]
[0122] Visually, inversion model 2 is closer to the true model than model 1. However, in Table 1, if we look at the RMSE index, model 1 has a lower RMSE than model 2, indicating that model 1 is superior, which contradicts subjective human judgment. If we look at the IOU and IRE indices, model 2 has both higher IOU and IRE than model 1, indicating that model 2 is superior, which aligns with subjective human judgment. Therefore, it can be seen that using only RMSE for evaluation may lead to incorrect judgments in certain situations.
[0123] As can be seen from Table 1, the IOU evaluation index of both inversion model 3 and inversion model 4 is the maximum value of 1, indicating that the shapes of the two inversion models are consistent with the true models. However, from... Figure 3 As can be seen, the shapes of the two inversion models are actually quite different. Therefore, the IOU evaluation index alone cannot select the better inversion model. However, according to the RMSE evaluation index, the RMSE of inversion model 4 is smaller, indicating that the amplitude of inversion model 4 is closer to the real model.
[0124] Therefore, relying solely on the IOU or RMSE evaluation metrics is inaccurate, but the IRE evaluation metrics provided in this embodiment can make a more accurate judgment.
[0125] In the magnetization vector inversion process, this method divides the magnetization vector into three directions for simultaneous inversion based on a three-component model. Furthermore, the three-component model is iteratively solved based on an objective function, which includes not only sensitivity-weighted constraints to counteract the depth-dependent attenuation of magnetic data but also a sparse Lp constraint matrix W for amplitude constraints. L_A By applying the objective function to the gradient of the three-component model, the edge accuracy of the inversion model obtained by the three-component model can be significantly improved, that is, the inversion result can produce sharp edges and the accuracy of the inversion result can be higher; and by using the evaluation factor that combines RMSE and IOU to evaluate the inversion result, more accurate evaluation results can be obtained.
[0126] Reference Figure 4 The diagram illustrates a functional block diagram of a magnetization vector inversion device based on amplitude and gradient constraints provided in this embodiment. The device includes:
[0127] The acquisition module 100 is used to acquire the observation data of the observation model;
[0128] The prediction data calculation module 200 is used to determine the prediction data of the observation model based on the three-component model, wherein the three-component model is used to describe the magnetization intensity of the observation model in three Cartesian directions.
[0129] The calculation module 300 is used to calculate, based on the observation data of the observation model, a data weighting matrix describing the data noise level, and to calculate, respectively, a sensitivity weighting matrix to offset the attenuation of magnetic data with depth, and a sparse Lp constraint matrix based on the amplitude constraint of the three-component model.
[0130] The objective function determination module 400 is used to determine the objective function based on the data weighting matrix, the sensitivity weighting matrix, and the sparse Lp constraint matrix based on the amplitude constraint of the three-component model.
[0131] The update module 500 is used to minimize the objective function to obtain the updated three-component model;
[0132] The iterative solution module 600 is used to perform iterative solution based on the updated three-component model until the iterative process reaches a preset iterative state, output the trained three-component model, and use the trained three-component model to generate the inversion result of the observation model.
[0133] Optionally, the device further includes:
[0134] The inversion result generation module is used to generate inversion results based on the trained three-component model.
[0135] The evaluation module is used to evaluate the inversion results by combining the root mean square error and the cross-union ratio.
[0136] Optionally, the prediction data calculation module includes:
[0137] The forward operator computation unit is used to compute the forward operators in three Cartesian directions;
[0138] The prediction data calculation unit is used to obtain the prediction data of the observation model based on the product of the forward operators in the three Cartesian directions and the three-component model.
[0139] Optionally, the computing module includes:
[0140] An amplitude calculation unit is used to calculate the amplitude of the three-component model;
[0141] The first generation unit is used to combine the magnitude of the three-component model with the sparse Lp norm constraint function to generate the sparse Lp constraint matrix of the magnitude constraint of the three-component model.
[0142] Optionally, the iterative solution module includes:
[0143] The first iteration unit is used to iteratively solve the updated three-component model until the number of iterations is the maximum number of iterations for the three-component model, and then outputs the trained three-component model.
[0144] The second iteration unit is used to iteratively solve the updated three-component model until the change in the three-component model is minimized, and then outputs the trained three-component model.
[0145] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the magnetization vector inversion method based on amplitude and gradient constraints described in the embodiments.
[0146] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.
[0147] Those skilled in the art will understand that embodiments of this application can be provided as methods, apparatus, or computer program products. Therefore, embodiments of this application can take the form of entirely hardware embodiments, entirely software embodiments, or embodiments combining software and hardware aspects. Furthermore, embodiments of this application can take the form of computer program products implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.
[0148] This application describes embodiments with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0149] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0150] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0151] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.
[0152] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.
[0153] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.
Claims
1. A method of magnetization vector inversion based on amplitude and gradient constraints, characterized in that, The method comprises: acquiring observation data of a three-component model, and determining prediction data of the three-component model, wherein the three-component model is used to describe magnetization intensity in three Cartesian directions; respectively calculating a data weighting matrix used to describe data noise level, a sensitivity weighting matrix used to offset depth attenuation of magnetic data, and a sparse Lp constraint matrix based on amplitude constraint of the three-component model; determining a target function according to the observation data of the three-component model, the data weighting matrix, the sensitivity weighting matrix, and the sparse Lp constraint matrix based on the amplitude constraint of the three-component model, wherein the target function is applied to a gradient solving process of the three-component model; minimizing and solving the target function to obtain an updated three-component model; iteratively solving based on the updated three-component model until the iterative process reaches a preset iteration state, outputting a trained three-component model, and generating an inversion result of an observation model by using the trained three-component model.
2. The method of claim 1, wherein, The method further comprises: generating an inversion result according to the trained three-component model; evaluating the inversion result in combination with root mean square error and intersection over union.
3. The method according to claim 1 or 2, characterized in that, Determining prediction data of a three-component model comprises: calculating forward operators in three Cartesian directions; obtaining prediction data of the observation model according to a product of the forward operators in the three Cartesian directions and the three-component model.
4. The method of claim 1, wherein, Calculating a sparse Lp constraint matrix based on amplitude constraint of the three-component model comprises: calculating amplitude of the three-component model; generating the sparse Lp constraint matrix of the three-component model in combination with the amplitude of the three-component model and a sparse Lp norm constraint function.
5. The method of claim 4, wherein, The formula of the sparse Lp constraint matrix of the three-component model based on amplitude constraint is: wherein, is the amplitude of the three-component model; is a second threshold factor; p is a sparsity parameter; j is the jth 10m x 10m x 10m cubic cell after partitioning.
6. The method of claim 1, wherein, The formula of the sensitivity weighting matrix is: wherein, wherein, is a matrix is the element in the mth row and nth column; is a first threshold factor which is a small number; is a forward operator; m is the three-component model; is the volume of the jth cubic cell.
7. The method of claim 1, wherein, The formula of the target function according to the data weighting matrix, the sensitivity weighting matrix, and the sparse Lp constraint matrix based on the amplitude constraint of the three-component model is: wherein, denotes the objective function; is the data weighting matrix; is the sensitivity weighting matrix; is a sparse Lp constraint matrix based on the amplitude constraint of the three-component model; F is a forward operator in three Cartesian directions; m is the three-component model; is the observed data of the three-component model; is a regularization term coefficient, is an integral volume, is a discrete difference operator; is a reference model; c is a collective term for u, v, w, u, v, w represent three Cartesian directions; r is a collective term for s, x, y, z, s represents the model itself, x, y, z represent the components of the model in the three directions of xyz.
8. The method of claim 1, wherein, Iteratively solving based on the updated three-component model until the iterative process reaches a preset iteration state, outputting a trained three-component model, comprises: iteratively solving based on the updated three-component model until the number of iterations is the maximum number of iterations of the three-component model, outputting a trained three-component model; or, iteratively solving based on the updated three-component model until the change of the three-component model is the minimum, outputting a trained three-component model.
9. A magnetization vector inversion apparatus based on amplitude and gradient constraints, characterized by, The device comprises: an acquisition module configured to acquire observation data of a three-component model; a prediction data calculation module configured to determine prediction data of the three-component model, wherein the three-component model is used to describe magnetization intensity in three Cartesian directions; a calculation module configured to respectively calculate a data weighting matrix used to describe data noise level, a sensitivity weighting matrix used to offset depth attenuation of magnetic data, and a sparse Lp constraint matrix based on amplitude constraint of the three-component model; A target function determination module is configured to determine a target function according to the observation data of the three-component model, the data weighting matrix, the sensitivity weighting matrix, and a sparse Lp constraint matrix based on the amplitude constraint of the three-component model, wherein the target function is applied to a gradient solving process of the three-component model; An updating module is configured to minimize the target function to obtain an updated three-component model; An iterative solving module is configured to perform iterative solving based on the updated three-component model until the iterative process reaches a preset iteration state, output a trained three-component model, and generate an inversion result of an observation model by using the trained three-component model.
10. A computer-readable storage medium, characterized in that, The computer program is stored on the computer readable storage medium and is executed by the processor to implement the magnetization vector inversion method based on amplitude and gradient constraints according to any one of claims 1 to 8.